Anderson localization crossover in two-dimensional Si systems: The past and the present

Using the Ioffe-Regel-Mott criterion for strong localization crossover in disordered doped two-dimensional (2D) electron systems, we theoretically study the relationships between the three key experimentally determined localization quantities: critical density n(c), critical resistance rho(c), and sample quality defined by the effective impurity density (as experimentally diagnosed by the sample mobility mu(m) at densities much higher than critical densities). Our results unify experimental results for 2D metal-insulator transitions (MITs) in Si systems over a 50-year period (1970-2020), showing that n(c) (rho(c)) decreases (increases) with increasing sample quality, explaining why the early experiments in the 1970s, using low-quality samples [mu(m) similar to 10(3) cm(2)/(V s)], reported strong localization crossover at n(c) similar to 10(12) cm(-2) with rho(c) similar to 10(3) Omega whereas recent experiments (after 1995), using high-quality samples [mu(m) > 10(4) cm(2) /(V s)], report n(c) similar to 10(11) cm(-2) with rho(c) > 10(4) Omega. Our theory establishes the 2D MIT to be primarily a screened Coulomb disorder-driven strong localization crossover phenomenon, which happens at different sample-dependent critical density and critical resistance values, thus unifying Si 2D MIT phenomena over a 50-year period.